Superflip

The superflip is a famous position of the 3x3x3 where all corners are solved, and all edges are in the correct location but flipped. Despite its symmetry, this is an extremely difficult pattern, which is known to require 20 moves HTM to solve (in fact it was the first position that was proven to require that many moves). No position exists that requires more than 20 moves (see God's Number).

The superflip also has a few interesting properties because of the way it interacts with the Rubik's Cube Group. If you do a commutator with the superflip and any other algorithm, you will always end up back at the solved state; the superflip is also self-inverse, which means doing it twice will bring you back to the solved state. Also, because the superflip is completely symmetrical but not solved, any move will bring it to a position that is easier to solve.

One optimal solution in HTM for the superflip is U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2. The superflip also requires a minimum of 24 quarter turns to solve, and a minimum of 16 slice turns. One example of an optimal solution which requires 16 slice turns is S U B2 D2 M D' M2 S U R2 D M2 U B2 U S2. Another solution which requires 24 turns STM is MU'MU'MU'MU'yz'MU'MU'MU'MU'yz'MU'MU'MU'MU'. This is particularly easy to remember, as it is simply (MU')x4 followed by a yz'. This is repeated three times.